quape3 {lmomco} | R Documentation

## Quantile Function of the Pearson Type III Distribution

### Description

This function computes the quantiles of the Pearson Type III distribution given parameters (μ, σ, and gamma) of the distribution computed by `parpe3`. The quantile function of the distribution has no explicit form (see `cdfpe3`).

For the implementation in the lmomco package, the three parameters are μ, σ, and gamma for the mean, standard deviation, and skew, respectively. Therefore, the Pearson Type III distribution is of considerable theoretical interest to this package because the parameters, which are estimated via the L-moments, are in fact the product moments. Although, these values fitted by the method of L-moments will not be numerically equal to the sample product moments. Further details are provided in the examples section of the `pmoms` function documentation.

### Usage

    quape3(f, para)

### Arguments

`f` | Nonexceedance probability (0 <= F <= 1).
`para` | The parameters from `parpe3` or similar.

### Value

Quantile value for nonexceedance probability F.

### Author(s)

W.H. Asquith

### References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

### See Also

`cdfpe3`, `parpe3`

### Examples

      lmr <- lmom.ub(c(123,34,4,654,37,78))
      quape3(0.5,parpe3(lmr))

[Package lmomco version 0.92 Index]